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#1 2009-09-05 10:38:54
- tony123
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Find all pairs
Find all pairs (a,b) of integers
such that
Last edited by tony123 (2009-09-05 10:39:25)
#2 2009-09-06 11:25:04
- Fruityloop
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Re: Find all pairs
I don't believe there are any integers because...
Last edited by Fruityloop (2009-09-06 11:32:52)
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#3 2009-09-06 15:24:19
- bobbym
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Re: Find all pairs
Hi;
There are at least 2 solutions in Z
a=18 , b=3
a=3 , b=18
There may be more...
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#4 2009-09-06 22:46:48
- Fruityloop
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Re: Find all pairs
Good job Bobbym!
Oops...boy was I wrong.
(a+b)(a^2-ab+b^2)=3(2007-ab) doesn't mean (a+b)=3 or (a^2-ab+b^2)=3 
Last edited by Fruityloop (2009-09-06 22:54:52)
Help slow global warming. Drive a prius.
July 2012 was the hottest month ever for the U.S.
#5 2009-09-06 23:11:47
- bobbym
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Re: Find all pairs
Hi Fruityloop;
I am stuck on this one too.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#6 2009-10-28 04:20:20
- bobbym
- Administrator
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Re: Find all pairs
Hi Tony123;
Prove:
That shows that 6021 can be factored into an integer square and another term. Also there are no negative solutions (If b were negative b^2 would of course be positive)
We could either try all 8 factors 2 at a time or notice that one factor has to be a square. Only 1 and 9 are possible. 1 doesn't work but 9 does. b^2 = 9 -> b=3.
The only solutions are:
3,18 and 18,3.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.